The E Lydian dominant scale has 7 notes: E – F♯ – G♯ – A♯ – B – C♯ – D. Lydian dominant (the overtone scale) is Mixolydian with a raised 4th, or Lydian with a ♭7. It is the jazz sound over a 7♯11 chord and the bright “Simpsons theme” sound.
Compared with the E major scale it has ♯4 (A♯ instead of A), ♭7 (D instead of D♯).
The explorer above is set to E Lydian dominant: the whole neck is mapped, and you can zoom into any of its 7 positions, change the labels to degrees or fingers, and hear it up, down and in patterns.